Topic 1: Exponents And Radicals - Mathematics Notes Form Two


Welcome to our website darasahuru.co.tz, in this post you will find Topic 1: Exponents And Radicals - Mathematics Notes Form Two, form one mathematics notes, download notes for form one mathematics, PDF Exponents And Radicals Free Download

Topic 1: Exponents And Radicals - Mathematics Notes Form Two


Exponents


Exponents tell how many times to use a number itself in multiplication. There are different laws that guides in calculations involving exponents. In this chapter we are going to see how these laws are used.


EXPONENTS AND RADICALS

Indication of power, base and exponent is done as follows:

EXPONENTS AND RADICALS

Solution:

EXPONENTS AND RADICALS

To write the expanded form of the following powers:

EXPONENTS AND RADICALS

Solution

EXPONENTS AND RADICALS

To write each of the following in power form:

EXPONENTS AND RADICALS

Soln.

EXPONENTS AND RADICALS

The Laws of Exponents

List the laws of exponents

First law:Multiplication of positive integral exponent


Second law: Division of positive integral exponent


Third law: Zero exponents


Fourth law: Negative integral exponents


Verification of the Laws of Exponents


Verify the laws of exponents


First law: Multiplication of positive integral exponent


EXPONENTS AND RADICALS

Generally, when we multiply powers having the same base, we add their exponents. If x is any base and m and n are the exponents, therefore:


Example 1

EXPONENTS AND RADICALS

Solution

EXPONENTS AND RADICALS

If you are to write the expression using the single exponent, for example,(63)4.The expression can be written in expanded form as:

EXPONENTS AND RADICALS

Generally if a and b are real numbers and n is any integer,


Example 2

EXPONENTS AND RADICALS

Example 3


Example 4

EXPONENTS AND RADICALS

Generally, (xm)= X(mxn)

Example 5

Rewrite the following expressions under a single exponent for those with identical exponents:

EXPONENTS AND RADICALS

Second law: Division of positive integral exponent

Example 6

EXPONENTS AND RADICALS


shuletz.com


EXPONENTS AND RADICALS

Therefore, to divide powers of the same base we subtract their exponents (subtract the exponent of the divisor from the exponent of the dividend). That is,


where x is a real number and x ≠ 0, m and n are integers. m is the exponent of the dividend and n is the exponent of the divisor.

Example 8
EXPONENTS AND RADICALS

solution

EXPONENTS AND RADICALS

Third law: Zero exponents

Example 9

EXPONENTS AND RADICALS

This is the same as:

EXPONENTS AND RADICALS

If a ≠ 0, then

EXPONENTS AND RADICALS

Which is the same as:

EXPONENTS AND RADICALS

Therefore if x is any real number not equal to zero, then X0 = 1,Note that 00is undefined (not defined).


Fourth law: Negative integral exponents


EXPONENTS AND RADICALS

Also;

EXPONENTS AND RADICALS

Example 10

EXPONENTS AND RADICALS

Exercise 1

1. Indicate base and exponent in each of the following expressions:

EXPONENTS AND RADICALS

2. Write each of the following expressions in expanded form:

EXPONENTS AND RADICALS

3. Write in power form each of the following numbers by choosing the smallest base:

  1. 169
  2. 81
  3. 10,000
  4. 625

a. 169 b. 81c. 10 000 d. 625

4. Write each of the following expressions using a single exponent:

EXPONENTS AND RADICALS

5. Simplify the following expressions:


6. Solve the following equations:


7. Express 64 as a power with:

  1. Base 4
  2. Base 8
  3. Base 2
Base 4 Base 8 Base 2

8. Simplify the following expressions and give your answers in either zero or negative integral exponents.


9. Give the product in each of the following:


10. Write the reciprocal of the following numbers:

EXPONENTS AND RADICALS

Laws of Exponents in Computations

Apply laws of exponents in computations

Example 11


Solution

EXPONENTS AND RADICALS

Re-arranging Letters so that One Letter is the Subject of the Formula

Re-arrange letters so that one letter is the subject of the formula

A formula is a rule which is used to calculate one quantity when other quantities are given. Examples of formulas are:


EXPONENTS AND RADICALS

EXPONENTS AND RADICALS

Example 14

From the following formulas, make the indicated symbol a subject of the formula:

EXPONENTS AND RADICALS

Solution

EXPONENTS AND RADICALS

Transposing a Formulae with Square Roots and Square


Transpose a formulae with square roots and square


Make the indicated symbol a subject of the formula:


EXPONENTS AND RADICALS

Exercise 3

1. Change the following formulas by making the given letter as the subject of the formula.

EXPONENTS AND RADICALS

2. Use mathematical tables to find square root of each of the following:

EXPONENTS AND RADICALS

Previous Post Next Post

نموذج الاتصال